Influence of a simple pole on the convergence of separate node ascending derivatives expansion (SNADE) on a sequence of nodes alternating between 2 values

2018 ◽  
Vol 41 (17) ◽  
pp. 7333-7350 ◽  
Author(s):  
Derya Bodur ◽  
Metin Demiralp
Keyword(s):  
Simple Pole

scholarly journals Flexible simple-pole expansion of distribution functions

1997 ◽  
Vol 4 (10) ◽  
pp. 3469-3476 ◽  
Author(s):  
T. Löfgren ◽  
H. Gunell
Keyword(s):  
Distribution Functions ◽  
Simple Pole

scholarly journals Extremal Problems for Functions Starlike in the Exterior of the Unit Circle

1962 ◽  
Vol 14 ◽  
pp. 540-551 ◽  
Author(s):  
W. C. Royster
Keyword(s):  
Unit Circle ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Extremal Problems ◽  
Simple Pole ◽  
Image Position ◽  
Inverse Functions ◽  
Variational Formulas

Let Σ represent the class of analytic functions(1)which are regular, except for a simple pole at infinity, and univalent in |z| > 1 and map |z| > 1 onto a domain whose complement is starlike with respect to the origin. Further let Σ- 1 be the class of inverse functions of Σ which at w = ∞ have the expansion(2).In this paper we develop variational formulas for functions of the classes Σ and Σ- 1 and obtain certain properties of functions that extremalize some rather general functionals pertaining to these classes. In particular, we obtain precise upper bounds for |b2| and |b3|. Precise upper bounds for |b1|, |b2| and |b3| are given by Springer (8) for the general univalent case, provided b0 =0.

scholarly journals Remarks on the Elliptic Case of the Mapping Theorem for Simply-Connected Riemann Surfaces

1955 ◽  
Vol 9 ◽  
pp. 17-20 ◽  
Author(s):  
Maurice Heins
Keyword(s):  
Riemann Surface ◽  
Meromorphic Function ◽  
Riemann Surfaces ◽  
Simple Pole ◽  
Conformal Map ◽  
Elliptic Case ◽  
Extended Plane ◽  
Simply Connected ◽  
Conformal Equivalence

It is well-known that the conformal equivalence of a compact simply-connected Riemann surface to the extended plane is readily established once it is shown that given a local uniformizer t(p) which carries a given point p0 of the surface into 0, there exists a function u harmonic on the surface save at p0 which admits near p0 a representation of the form(α complex 0; h harmonic at p0). For the monodromy theorem then implies the existence of a meromorphic function on the surface whose real part is u. Such a meromorphic function has a simple pole at p0 and elsewhere is analytic. It defines a univalent conformal map of the surface onto the extended plane.

A Simple Pole in Ithaca, NY

2016 ◽  
Vol 9 (0) ◽  
Author(s):  
Daniel W. Stroock
Keyword(s):  
Simple Pole

scholarly journals On the Tumura-Clunie Theorem and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Gaixian Xue ◽  
Jinjin Huang
Keyword(s):  
Meromorphic Functions ◽  
Simple Pole

We cast aside the restriction of the simple pole in the Tumura-Clunie type theorems for meromorphic functions and obtain a better result which improves the earlier results of Y. D. Ren. Furthermore, as an application, we improve a theorem given by B. Y. Su.

scholarly journals Two numerical methods for Abel's integral equation with comparison

2012 ◽  
Vol Volume 15, 2012 ◽  
Author(s):  
Abdallah Ali Badr
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Fractional Order ◽  
Quadrature Formula ◽  
Approximate Formula ◽  
Simple Pole ◽  
Numerical Examples ◽  
International Audience ◽  
Modified Formula

International audience Analogy between Abel's integral equation and the integral of fractional order of a given function, j^α f(t), is discussed. Two different numerical methods are presented and an approximate formula for j^α f(t) is obtained. The first approach considers the case when the function, f(t), is smooth and a quadrature formula is obtained. A modified formula is deduced in case the function has one or more simple pole. In the second approach, a procedure is presented to weaken the singularities. Both two approaches could be used to solve numerically Abel's integral equation. Some numerical examples are given to illustrate our results.

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